document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129801>Question 129801</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9. Ticket Sales. The number of tickets sold each day for<BR>\n" );
document.write( "an upcoming performance of Handel’s Messiah is<BR>\n" );
document.write( "given by<BR>\n" );
document.write( ",N(x) -0.4x^2+9x+11<BR>\n" );
document.write( "where x is the number of days since the concert was<BR>\n" );
document.write( "first announced. When will daily ticket sales peak and<BR>\n" );
document.write( "how many tickets will be sold that day? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94793 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=94793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28x%29+-.4x%5E2+%2B+9x+%2B+11 ALIGN=MIDDLE  ALT=\"N%28x%29+-.4x%5E2+%2B+9x+%2B+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a parabola that peaks at the <BR>\n" );
document.write( "midpoint of the 2 roots which are<BR>\n" );
document.write( "found by applying the formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can decompose this into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-b%29%2F%282a%29+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29%2F%282a%29+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-b%29%2F%282a%29+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-b%29%2F%282a%29+-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%2F%282a%29+ ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-b%29%2F%282a%29+-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The midpoint of these is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28b%2F2a%29 ALIGN=MIDDLE  ALT=\"-%28b%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The equation is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-.4 ALIGN=MIDDLE  ALT=\"a+=+-.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+9 ALIGN=MIDDLE  ALT=\"b+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28b%2F2a%29+=+-%289%2F%282%2A%28-.4%29%29%29 ALIGN=MIDDLE  ALT=\"-%28b%2F2a%29+=+-%289%2F%282%2A%28-.4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28b%2F2a%29+=+9%2F.8 ALIGN=MIDDLE  ALT=\"-%28b%2F2a%29+=+9%2F.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28b%2F2a%29+=+11.25 ALIGN=MIDDLE  ALT=\"-%28b%2F2a%29+=+11.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is days after concert starts when the ticket sales peak<BR>\n" );
document.write( "when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28x%29 ALIGN=MIDDLE  ALT=\"N%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28x%29+-.4x%5E2+%2B+9x+%2B+11 ALIGN=MIDDLE  ALT=\"N%28x%29+-.4x%5E2+%2B+9x+%2B+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%2811.25%29+=+-.4%2A11.25%5E2+%2B+9%2A11.25+%2B+11 ALIGN=MIDDLE  ALT=\"N%2811.25%29+=+-.4%2A11.25%5E2+%2B+9%2A11.25+%2B+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%2811.25%29+=+-50.625+%2B+101.25+%2B+11 ALIGN=MIDDLE  ALT=\"N%2811.25%29+=+-50.625+%2B+101.25+%2B+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%2811.25%29+=+61.625 ALIGN=MIDDLE  ALT=\"N%2811.25%29+=+61.625\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the daily tickets sales peak<BR>\n" );
document.write( "I'll plot the equation to check<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-5%2C+26%2C+-5%2C+65%2C+-.4x%5E2+%2B+9x+%2B+11%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-5%2C+26%2C+-5%2C+65%2C+-.4x%5E2+%2B+9x+%2B+11%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );